Publications

Preprints

• Regularization for Multi-Phase 2D Euler Equations via Competing Transport Markers. (2026) (arXiv) 

• Validity of Prandtl's boundary layer from the Boltzmann theory, with Chanwoo Kim. (2024)(arXiv) (Submitted to CPAM).

Journal Publications

• Asymptotics of Helmholtz-Kirchhoff Point-Vortices in the Phase Space, with Chanwoo Kim.  – Commun. Math. Phys. (2025)(pdf)(Journal).

• The Feynman-Lagerstrom criterion for boundary layers, with Theodore D. Drivas and Sameer Iyer. – Arch. Ration. Mech. Anal. (2024)(pdf)(Journal).

• The inviscid limit of Navier-Stokes equations for locally near boundary analytic data on an exterior circular domain, with Toan T. Nguyen. Commun. Math. Phys. (2024) (pdf)(Journal).

• The inviscid limit for the 2d Navier-Stokes equations in bounded domains, with Claude W. Bardos, Toan T. Nguyen, and Edriss S. Titi. –  Kinetic and Related Models (2022)(pdf)(Journal).

• On the Euler+Prandtl expansion for the Navier-Stokes equations, with Igor Kukavica, Vlad Vicol, and Fei Wang. – J. Math. Fluid Mech.(2022)(pdf)(Journal).

• Derivative estimates for screened Vlasov-Poisson system around Penrose-stable equilibria – Kinetic and Related Models. (2020)(pdf)(Journal).

• The inviscid limit of Navier-Stokes with critical Navier-slip boundary conditions for analytic data – SIAM J. Math. Anal. (2020)(pdf)(Journal).

• The inviscid limit of Navier-Stokes equations for vortex-wave data on R2, with Toan T. Nguyen –SIAM J. Math. Anal. (2019)(pdf)(Journal).

• The inviscid limit of Navier-Stokes equations for analytic data on the half-space, with Toan T. Nguyen –Arch. Ration. Mech. Anal. (2018)(pdf)(Journal).

Expository Notes:

• Deep Learning Architectures: From Perceptrons to GPT-3 (2026)

• Measure Theory (2012) (link)